SAT fractions

Hi, I was doing some problems in an SAT math workbook and came across this:
(all parentheses added by me to deter confusion)
1/(1+1/b) = p Which expression is 2p?
The answer given by the book is 1/ ((1/2)+(1/2b))

However, it would seem to me if p=1/(1+1/b) then 2p=2(1/(1+1/b)) = 2/(2(1+1/b)) = 2/(2+2/b)

Hi, I was doing some problems in an SAT math workbook and came across this:
(all parentheses added by me to deter confusion)
1/(1+1/b) = p Which expression is 2p?
The answer given by the book is 1/ ((1/2)+(1/2b))

However, it would seem to me if p=1/(1+1/b) then 2p=2(1/(1+1/b)) = 2/(2(1+1/b)) = 2/(2+2/b)

Thanks Skeeter for the reply. I understand now how the book got the answer 1/ ((1/2)+(1/2b)). But I still don't understand logically why if p = something that 2*p = 2*something doesn't work. I know I'm probably just missing something incredibly stupid, but I just don't get it.

Thanks Skeeter for the reply. I understand now how the book got the answer 1/ ((1/2)+(1/2b)). But I still don't understand logically why if p = something that 2*p = 2*something doesn't work. I know I'm probably just missing something incredibly stupid, but I just don't get it.

it works, but you did not work it correctly ...

However, it would seem to me if p=1/(1+1/b) then 2p=2(1/(1+1/b)) = 2/(2(1+1/b)) = 2/(2+2/b)

I knew I was doing something stupid! It's 2/1 * 1/(1+1/b). Now can you explain to me why the answer is 1/(1/2+1/2b) not 2/(1+1/b). It's probably something stupid again, but I really appreciate the help.